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# Secret codes

In this video, Dr. Yossi Elran explains about the connection between mathematical operators and two kinds of secret codes.

This is where all that we have learnt comes together. Secret codes. First, to get a brief introduction, please take time to watch the short video.

Secret codes can be viewed as a symbology, except that now different symbols encode letters instead of numbers. These symbols can be signs (like Morse code or Braille which are just encodings and not ‘secret’), or they can be other letters, or even the same letters themselves.

One can encode a message letter by letter, exchanging each letter with another symbol (these are substitution ciphers), or one can encode the whole message by scrambling up the order of the letters in the message (transposition ciphers).

But when we encrypt a message what are we really doing? We are operating on text with an operator that transforms the text into another symbology.

And when we want to try and break a code we have to work out what the symbology is and also what the encoding operator does. In other words, given an illegible encoded text, we have to work out what the operator is – is it a substitution cipher or a transposition cipher and how does the operator work? And we also have to work out the symbology in order to ‘break’ the secret code.

Cryptography is a huge topic in mathematics with many day-to-day applications, that deserves a full-fledge course. Still, I would like to challenge you with two secret codes, one a transposition and the other a substitution code that I have made up and see if you can ‘break’ the codes. I’m just going to give you the secret messages, and you can ‘break’ them for yourselves. I also have a special request – make up your own secret code, write it down in the discussion and let us all try and ‘break’ the codes. Here are my two:

Message 1:

TELLH NAROW OIANY WTEEO DTEVO HKMTI
WLSWE YUERI EOHNI ITIRO PTLGA NEKNT
AWWUA HDHDD SLKTR OHABE SLIIK

HINT: First create an empty rectangular box 15×6. The first column of the rectangular box should contain 15 letters, the other columns should contain only 14 letters.

Message 2:

PDUBK DGDOL WWOHO DPEOL WWOHO DPEOL WWOHO DPEPD UBKDG DOLWW OHODP ELWVI OHHFH ZDVZK LWHDV VQRZ

Good Luck!